SOLUTION: A rectangle is twice as long as it is wide. If the length is increased by 4 cm and its width is decreased by 3 cm, the new rectangle formed has an area of 100 sq cm. Find the dimen

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Question 1004773: A rectangle is twice as long as it is wide. If the length is increased by 4 cm and its width is decreased by 3 cm, the new rectangle formed has an area of 100 sq cm. Find the dimensions of the original rectangle.
Answer by addingup(3677) About Me  (Show Source):
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L= 2W
(2W+4)(W-3)= 100
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Solve for W:
(W-3) (2 W+4) = 100
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Expand out terms of the left hand side:
2W^2-6W+4W-12 = 100 Add subtract on left:
2W^2-2W-12= 100
Divide both sides by 2:
W^2-W-6 = 50 Fa
Add 6 to both sides:
W^2-W = 56
Subtract 56 on both sides:
W^2-W-56= 0 Factor the equation: 7*8= 56 and 8-7= 1
(W-8)(W+7)= 0
Split into 2 equations:
W-8= 0 or W+7= 0
W= 8 or W= -7 Toss the -7, we are not looking for a negative number.
Our width is 8. Proof:
(2W+4)(W-3)= 100
((2*8)+4)(8-3)= 100
20*5= 100
100=100 We've got the right answer